“The difficulty with modeling markets in a dynamical way is that their essence is free human choice, while the central core of dynamical systems is determinism.“Determinism” means that the past determines the future and as will be demonstrated, vice versa.”

The author then delves into some abstract algebra and topology, all of which is essentially encapsulated in a diagram. The author concludes with these words:

“Backtesting typically withholds a subsample of the data and uses it to simulate prediction, usually from the most recent past. This subsample choice implicitly assumes that the influence of the distant past decays quickly, or essentially the same information is embedded in the recent past. If this is wrong, backtests may indicate good training period performance against simulation data, but the model has poor trading performance in even the immediate future.

The backtest procedure below provides some insight into the degree of unpredictability, if the conjecture holds. First, create two simulation buckets. One bucket contains data from the recent past while the other bucket contains data from further back in time. A stationary process implies that model simulation is equally good (statistically speaking) for both buckets given appropriate sample size and model selection. If the converse true, it has far-reaching consequences.”

All of this is the essence of why trading is so difficult. What ever statistical distributions hold for some period in the past, they do not necessarily hold in the future. Do we then have to consider distributions of distributions? Or maybe distributions of distributions of distributions? Maybe this quickly leads to infinite regress. While such considerations can quickly lead to despair, there is a way out. If distributions are changing, then models must be recalibrated at some frequency in an attempt to capture the changing nature of the underlying statistical distribution of asset price movements. Another approach is to construct a system that automatically adapts to changing distributions.

My cybernetic system attempts to accomplish the latter. One way that the system is able to accomplish this is by taking a long term view of the markets to capture long term trends in asset prices while ignoring shorter term volatility. The cybernetic system will not capture every change in underlying distributions and it will lag behind such changes, hence it will have draw downs. However, the idea is that the system has sufficient adaptivity to capture most of the major changes in a sufficiently timely manner to be profitable.

I am currently doing some very preliminary work on two systems that will attempt to react much faster to changing distributions via frequent recalibration. My day job will be quite hectic for the next few weeks, so I won’t have as much time as I would like to work on these systems. Hopefully, when things settle down, I will be able to generate results in the not too distant future.